منابع مشابه
Dense resultant of composed polynomials: Mixed-mixed case
The main question of this paper is: What is the dense (Macaulay) resultant of composed polynomials? By a composed polynomial f ◦ (g1, . . . , gn), we mean the polynomial obtained from a polynomial f in the variables y1, . . . , yn by replacing yj by by some polynomial gj . Cheng, McKay and Wang and Jouanolou have provided answers for two particular subcases. The main contribution of this paper ...
متن کاملCayley-Dixon Resultant Matrices of Multi-univariate Composed Polynomials
The behavior of the Cayley-Dixon resultant construction and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each variable is substituted by a univariate polynomial in a distinct variable. It is shown that a Dixon projection operator (a multiple of the resultant) of the composed system can be expressed as a power of the...
متن کاملSparse Resultant of Composed Polynomials IMixed-. Unmixed Case
The main question of this paper is: What happens to sparse resultants under composition? More precisely, let f1, . . . , fn be homogeneous sparse polynomials in the variables y1, . . . , yn and g1, . . . , gn be homogeneous sparse polynomials in the variables x1, . . . , xn. Let fi ◦ (g1, . . . , gn) be the sparse homogeneous polynomial obtained from fi by replacing yj by gj . Naturally a quest...
متن کاملResultant and Discriminant of Polynomials
This is a collection of classical results about resultants and discriminants for polynomials, compiled mainly for my own use. All results are well-known 19th century mathematics, but I have not investigated the history, and no references are given. 1. Resultant Definition 1.1. Let f(x) = anx n + · · ·+ a0 and g(x) = bmx + · · ·+ b0 be two polynomials of degrees (at most) n and m, respectively, ...
متن کاملOn the resultant of degree-deficient polynomials
The resultant is an algebraic expression, computable in a finite number of arithmetic operations from the coefficients of two univariate polynomials, that vanishes if, and only if, the two polynomials have common zeros. The paper considers formal resultant for degree-deficient polynomials (polynomials whose actual degree is lower than their assumed degree). Some key properties of the resultant ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2003
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(03)00039-7